A) \[\sqrt{3}\,\,\tan 8{}^\circ \]
B) \[\sqrt{3}\cot 8{}^\circ \]
C) \[\sqrt{3}\,\,\sin 38{}^\circ \]
D) \[\sqrt{3}\,\,\sin 8{}^\circ \]
Correct Answer: A
Solution :
| \[\frac{\sin 38{}^\circ -\cos 68{}^\circ }{\cos 68{}^\circ +\sin 38{}^\circ }=\frac{\text{cosec}52{}^\circ -\cos 68{}^\circ }{\cos 68{}^\circ +\cos 52{}^\circ }\] |
| \[=\frac{2\sin \left( \frac{52{}^\circ +68{}^\circ }{2} \right)\sin \left( \frac{68{}^\circ -52{}^\circ }{2} \right)}{2\cos \left( \frac{52{}^\circ +68{}^\circ }{2} \right)\cos \left( \frac{68{}^\circ -52{}^\circ }{2} \right)}\] |
| \[=\frac{\sin 60{}^\circ \cdot \sin 8{}^\circ }{\cos 60{}^\circ \cdot \cos 8{}^\circ }=\tan 60{}^\circ \cdot \tan 8{}^\circ =\sqrt{3}\tan 8{}^\circ \] |
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